A company produces three products every day. Their production on a certain day is 45 tons. It is found that the production of the third product exceeds the production of a first product by 8 tons while the total production of a first and third product is twice the production of the second product. Determine the production level of each product using the matrix method.
Let the numbers are x, y, z
x + y + z = 45 ……(i)
Also,
Z – x = 8 ……(ii)
Again,
x + z = 2y …… (iii)
A X = B
|A| = 1(2) – 1(– 2) + 1(2)
= 6
Hence, the unique solution given by x = A – 1B
C11 = (– 1)1 + 1 (0 + 2) = 2
C12 = (– 1)1 + 2 (– 1 – 1) = 2
C13 = (– 1)1 + 3 (2 – 0) = 2
C21 = (– 1)2 + 1 (1 + 2) = – 3
C22 = (– 1)2 + 2 (1 – 1) = 0
C23 = (– 1)2 + 3 (– 2 – 1 ) = 3
C31 = (– 1)3 + 1 (1 – 0) = 1
C32 = (– 1)3 + 2 (1 + 1) = – 2
C33 = (– 1)3 + 3 (0 + 1) = 1
X = A – 1 B = 
Adj A = 
X = 
X = 
= 
Hence, x = 11, y = 15 and z = 19